I have a heavy pdf which I need to revise, and I massively need the tool "Search and replace all" with or without the option to revise the changes 1 by 1 (depends on grammar) in a quick and optimised workflow.

Which editor is the best for that, Acrobat Pro DC or Adobe illustrator? The pdf has a lot of text boxes and a peculiar formatting.

Acrobat doesn't have a Search and Replace All command, and I doubt Illustrator will too.

PDF files were simply not meant to be edited in such an extended way. You should go back to the original file used to create the PDF and edit it, or if you don't have access to that file export the PDF to another format and then edit it.

As mentioned earlier. PDF files are not meant to be extensively edited. PDF files are not Word Processing documents. Think of it as digital stone. If a stone has been text engraved in it you can fill it in and make changes, but it won't look the same as creating the stone over from scratch. You certainly don't want to change hundreds of stone tablets. If the original files are not available to recreate the pdf, you might try to save the PDF files to Word format and see if you can recreate the PDF. When you edit a PDF file, it is possible to change just one letter and have the entire page fall apart.